1. Orrin Kendall biscuits, which soldiers ate during the Civil War.
2. Short for Aux Cayes, a Haitian port that American sailors praised for its rum.
3. Old Keokuk, a Native American tribal chief who was said to have signed treaties with his initials.
4. OK stands for "all correct" or the illiterate phrase "Orl Korrect."
5. U.S. President Martin Van Buren's nickname "Old Kinderhook" -- OK for short. He was a native of Kinderhook, N.Y.
6. Choctaw word "okeh," (or "hoke") meaning "indeed" (or "It is so.")
7. Scottish "auch aye", meaning "ah yes." (Or "och aye," meaning "okay.")
8. From the French maritime phrase "au quai" meaning "at dock", and therefore at last safe from the ravages of the open sea.
9. '0 killed' - the report of the night's death toll during the First World War.
10. All clear after the shoot-out at O.K. Corral.
11. Instruments calibrated at an Observatory at Kew had, affixed to them, a stamp, or impression, to authenticate that calibration. This stamp was O K - Observatory Kew.

New origins from Mr. Rawson's book:
12. The abbreviation is for Oberst Kommandant, German for "Colonel in Command," used by either -- take your pick -- a General Schliessen or Baron von Steuben when initialing letters and orders during the American Revolution.
13. It comes from the name of a freight agent, Obadiah Kelly, whose initials were widely disseminated on bills of lading.
14. The abbreviation is for Open Key, popularized by telegraphers in the 1860s.
15. It comes from the names of Lords Onslow and Kilbracken, who initialed bills after they were read and approved in England's House of Lords.
16. From a misreading of "Order Recorded" on official documents.
17. Or from Finnish "oikea," correct.
18. From the Greek "olla," all, plus "Kalla," good.

Professor Allen Walker Read of Columbia University, "finally unveiled its (O.K.'s) origins in a series of magisterial articles in 'American Speech' in 1963 and 1964.What Professor Read discovered was that the abbreviation arose in a humorous manner at a time when Americans were indulging in a great deal of wordplay, including abbreviations, acronyms, puns and intentional mispronunciations and misspellings. The earliest example of O.K. that he unearthed (and it is so far still the oldest known specimen) is from the Boston 'Morning Post' of March 23, 1839. It appears in connection with a note by the paper's editor, Charles Gordon Greene, about a visit to New York of some members of the local Anti-Bell-Ringing Society. (The A.B.R.S., as it was usually known, was itself something of a joke, having been formed the previous year to oppose -- its name to the contrary -- an ordinance of the Boston Common Council against ringing dinner bells.) In an aside, Mr. Greene suggested that if the Bostonians were to return home via Providence, they might be greeted by one of his rivals, the editor of that city's 'Journal,' who 'would have the 'contribution box,' et ceteras, o.k. -- all correct -- and cause the corks to fly, like sparks, upward.'.Thus, it appears that O.K. was invented, possibly by Greene, as an abbreviation of the jocular 'Oll' or perhaps 'Orl korrect,' meaning "All right.' This explanation would seem farfetched, except for Read's finding that it dovetails with such coinages of the period as O.W. for 'All Right,' as though spelled 'Oll Wright' (this appeared in the Boston 'Morning Post' in 1838, the year before O.K.'s debut); K.G. for 'No Good'; and K.Y. for 'No Yuse.'."

So it looks like origin No. 4 is correct. Professor Read does believe that O.K. "certainly was popularized" by the use of Martin Van Buren's nickname, Old Kinderhook, (See No. 5) during the presidential campaign of 1840.